According to this general formalism the Dirac equation in the conformal frame \(\lbrace x_c;e\rbrace \)  of \(M_+\)  reads [1]}
\(\left[-i\omega _{H}t_c\left(\gamma ^0\partial _{t_c}+\gamma ^i\partial _{x^i_c}\right)+\frac{3i}{2}\omega _H\gamma ^{0}-m\right]\psi (t,{\bf x})=0\,,\) 
